I am currently attempting to use a bivariate normal distribution to identify the most likely range of movement for a blob in computer vision. This itself is not the problem, however; I do not understand how σ plays a role in finding discrete probability contours.
I am not permitted to post images yet since my reputation is too low, but here is a link to a the graph:
This is a sample contour plot from Mathematica which displays the Bivariate Probability Density Function with σX = .27 and σY = .54 . μX = 0, μY = 0, and ρ = 0.
I would appreciate it very much if someone could explicate what determines the contour ellipses and how I would go about calculating them for functions of variable σX and σY.